How do I use implicit differentiation

Question

find the derivative? 2√ y = x - y?

Answer 1

Given : 2√y = x - y

Differentiate with respect to x.

(d/dx) [2√y] = (d/dx)(x - y)

2[1/(2√y)](dy/dx) = 1 - (dy/dx)

Substitute y' = (dy/dx)

[1/(√y)] y'= 1 - y'

[(y^-½)] y'+ y' = 1

[y^-½ +1]y' = 1

y' = 1/[1+y^-½]

The solution is y' = 1/[1+y^-½]